Vol 61, No 7 (2025)

A family of conservative difference schemes for calculating viscous gas flows in arbitrary orthogonal curved coordinates is constructed on the basis of a cartesian Godunov-type difference scheme of a general type. At the same time, the algorithms for calculating the numerical flows of the basic scheme remain unchanged. It is shown that the schemes of the constructed family have a second order of approximation in space, provided that the numerical flows of the basic scheme are calculated with a second or higher order of accuracy.

The problem of mathematical modeling of the acceleration of metal conductors in an electromagnetic field in a two-dimensional approximation has been solved. Mathematical models are presented to describe the motion of bodies using Lagrangian and Eulerian coordinates using the constitutive relations of a thermoelastoplastic body (for the case of large deformations) and a viscous compressible fluid (gas). A mathematical model is presented that allows us to describe the movement of a body taking into account the presence of different phases of matter in it at one point in time. The model explicitly identifies the transition phase from solid to liquid; for this phase, both constitutive relations are taken into account, taken with appropriate weights. Numerical algorithms based on the finite element method have been constructed. The presented model is used to solve the problem of accelerating an aluminum cylindrical shell to a velocity of about 8 km/s. The calculation results are demonstrated, and individual characteristics are compared with known calculated and experimental results.

The fully conservative finite volume discretization of the incompressible Navier–Stokes equations in cylindrical coordinates is constructed on a staggered grid. The proposed discretization ensures momentum conservation in a computational domain, and mass conservation within the control volumes for pressure, and velocity components. The energy conservation equation directly follows from the discrete momentum equation. Both conservative and non-conservative forms of convective terms are approximated. The proposed discrete counterpart of the vector Laplace operator is self-adjoint and negative definite.

The paper is devoted to numerical studies of two-phase hyperbolic model describing the dynamics of hyperelastic media. The considered model is a generalization of the well known model of multivelocity fully nonequilibrium Baer–Nunziato model, widely used for description of shock-wave and detonation processes in multiphase media. The equations of the model are given both in the general and in the spatially one-dimensional case, and its properties are described. For numerical study, the pathconservative HLL method is applied. The numerical study is carried using a number of Riemann problems.

The paper considers the method of internal interval estimation of the information set of the problem of parametric identification of dynamic systems, when the experimental data are specified in the form of intervals. The state of the dynamic systems under consideration at each moment of time is a parametric set. The objective function is constructed in the space of interval estimates of parameters, characterizing the degree of inclusion of parametric sets of states in the specified experimental interval estimates of phase variables. An expression for the gradient of the objective function is obtained. The proposed approach consists of two stages. At the first stage, the objective function is minimized by first-order optimization methods, and at the second stage, the obtained estimate of the information set is successively expanded with control of the value of the objective function. To solve a variety of direct problems in the process of constructing the desired estimate, the adaptive interpolation algorithm previously developed by the authors is used. The efficiency and performance of the approach under consideration is demonstrated on a representative series of problems.